Question

Consider triangle ABC with M < C= 65, b  = 5 and 

c  = 6. Which option lists an expression that is equivalent to  m <B ?

Answer 1

Given:
m∠C = 65°
b = 5
c = 6

Apply the Law of Sines.
sin(B)/b = sin(C)/c
sin(B)/5 = sin(65)/6
sin(B) = (5*sin(65))/6 = 0.7553
B = arcsin(0.7553) = 49.05°

Answer: m∠B = arcsin(0.7553) = 49° (approx)